# Caplat et al. (in press) publication available online

Caplat P., Nathan R., and Buckley Y.  In press.  Seed terminal velocity, wind turbulence and demography drive the spread of an invasive tree in an analytical model. Ecology. [doi:10.1890/11-0820.1]

Summary provided by Dr. Paul Caplat.

We explained in an earlier post (http://buckleyplantecologylab.wordpress.com/2009/11/05/black-pine-project-2/) the raison d’etre and the objectives of our work in New Zealand. After one year of data analysis and model development, we are proud to publish the results of the study in Ecology.

I would advise anybody interested in population biology, seed dispersal, invasive management or mathematical ecology to read the abstract – or even the whole paper – but here are a few points that summarize the work:

• the demographic component (= population processes) of plant invasions has been successfully approached with analytical models
• so far the spatial component of plant invasions, seed dispersal, has been either approached with:
1. simulation models – highly detailed, but sometimes difficult to interpret, computation-intensive and not easy to generalize to other systems that the ones they are based on; and
2. analytical models  – easy to interpret, easy to run and very general, but address dispersal in a manner that does not account for precise mechanisms.
• [at this stage you should know what is coming] We developed a method to incorporate a precise, semi-mechanistic model of seed dispersal into simple, general, and easy to interpret analytical model. More specifically we combined two state-of-the art modeling approaches: (i) a complex but elegant mathematical modeling framework usually refered to as “the integrodifference equation model”, or more often “the Neubert-Caswell model” (it was published in 2000 by Mike Neubert and Hal Caswell), and (ii) an elegant but complex dispersal model that simplifies a highly complex dispersal model based on the physics of wind turbulence in forest canopies into a single mathematical equation, called WALD (Katul et al. 2005).
• we parameterized the model with the data from Mt Barker (see “black pine project”)
• our model matched accurately the pattern of invasion observed at Mt Barker
• our model allowed to give a precise and general quantification of the effect of different variables (such as seed release height, number of seeds produced, survival of adults, wind turbulence…) on the rate at which the pine population spread. Particularly, seed terminal velocity (the speed at which a seed fall in still air), a variable driven by different morphological features of seeds and very much species-specific, was consistently important in our analyses (oh yes, we did different analysis but that’s all in the paper) – see an example in the figure below.

Sensitivity and elasticity of spread rate, c*, to dispersal (dark grey columns) and demographic (light grey columns) parameters, in a model for Corsican pine invasion in a mountain of New-Zealand.  Dispersal parameters are: vt: seed terminal velocity; hr: height of seed release; hc: canopy height; Ū: mean horizontal windspeed; σw: standard deviation of vertical windspeed; κ: turbulence coefficient. See above for the demographic parameters.